A probabilistic particle approximation of the “Paveri-Fontana” kinetic model of traffic flow - Archive ouverte HAL Access content directly
Journal Articles SMAI Journal of Computational Mathematics Year : 2016

A probabilistic particle approximation of the “Paveri-Fontana” kinetic model of traffic flow

Abstract

This paper is devoted to the Paveri-Fontana model and its computation. The master equation of this model has no analytic solution in nonequilibrium case. We develop a stochastic approach to approximate this evolution equation. First, we give a probabilistic interpretation of the equation as a nonlinear Fokker- Planck equation. Replacing the nonlinearity by interaction, we deduce how to approximate its solution thanks to an algorithm based on a fictitious jump simulation of the interacting particle system. This algorithm is improved to obtain a linear complexity regarding the number of particles. Finally, the numerical method is illustrated on one traffic flow scenario and compared with a finite differences deterministic method.

Dates and versions

hal-01415636 , version 1 (13-12-2016)

Identifiers

Cite

Jyda Mint Moustapha, Benjamin Jourdain, Dimitri Daucher. A probabilistic particle approximation of the “Paveri-Fontana” kinetic model of traffic flow. SMAI Journal of Computational Mathematics, 2016, 2, pp.229-253. ⟨10.5802/smai-jcm.15⟩. ⟨hal-01415636⟩
180 View
0 Download

Altmetric

Share

Gmail Facebook Twitter LinkedIn More